## Is 0.9 recurring equal to 1?

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Midnight_Carnival
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### Re: Is 0.9 recurring equal to 1?

You like number-games, I like playing with words.

Look up "reification" (assuming I spelled it correctly [and that my political philosphy lecturer explained it right and that I understood him]).

---
Again, I want to point out the error I am seeing here.
treating numbers as things! However much it may be fun to show off how smart you are and how your facility for analytical forms for thought (which need I remind you are completely redundant since we have machines to do those things now) exceed those around you, it remains that numbers are not things. Numbers are abstract judgemnts which can be applied to things, much like "good" and "evil". We made up, and yes, we did make it up, it wasn't just a fact of life we discovered, numbers such as 1 becasue it is difficult to work with 0.999(rec) so we said "let that be 1" -we do it when we talk about "one nation", although this is comprised of many individuals, who may not feel any form of solidarity and who are in different places. "One race" although many of the people in that "race" wouldn't classify themselves as you have, "one type" - One is a convenient shortcut, an excuse for laziness, but many believe that one is real.
Trying to prove that 1 is real, whole, perfect, possible or has any meaning other than that which is ascribed to it by us at a given time, is analogous to using the bible to prove that god exists. One interacts with other numbers, AMAZING! that is exactly what it was designed to do.
One is a lie.
0 is real.

-thanks bye.
...apparenly we can't go with it or something.
Zarel
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### Re: Is 0.9 recurring equal to 1?

lol, you're right on the definition of reification as a logical fallacy, but you're wrong in that that's what we're doing.

Numbers are abstract concepts, though, but they're rigorous abstract concepts, not vague concepts like "good" and "evil".

I've said it often enough, but it bears repeating: Mathematics is the study of tautology. Therefore, mathematics is the only discipline in which absolute truth exists.

That 1 = 0.9~ is absolute truth. "Real" and "whole" are adjectives that are meaningless in this context, but the equation could certainly be described as perfect truth.

All that rambling that "one nation" etc may not be a unified construct does nothing to change the fact that 1 is a number with a rigorous abstract definition. It just means you're not applying it correctly (not to mention that the vague concept of unification is fairly tangential to the rigorous concept of the number 1).
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Darkmage
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### Re: Is 0.9 recurring equal to 1?

I got to agree, you can either define a number in quite a lot of ways, I mean, let's take the number 4, we can state 4=8/2, or 2², or 4=4'0~ as well 1=1'0~ and 0'9~=1 using a mathematical correct method(as explained a whole lot of posts before) it says it's correct to say 1=0.9~, the matter is not to use as argument like "I can't imagine that two things are the same.", since maths are an exact(well, however it is said it can never be wrong) science, and there does not matter if you think something is wrong or not, it is either wrong or not independently of human thoughts.

(Reminds me of 1984 George Orwell's, saying 2+2=5 because the great brother says so.)
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### Re: Is 0.9 recurring equal to 1?

If I write a symbol on a board then we must both be in agreement what precise meaning is represented by that symbol before any tautology can be established. In computer science, limitations of numeric storage are by necessity a consideration during implementation. So I would debate your assertion that there is no recognized area of mathematics where 0.9 recurring is not equal to 1.

Other than that tiny nitpick however, I totally agree with Zarel. Anyone who doesn't think 0.9 recurring is equal to 1 is either joking (as I was with my first post), trolling, or simply hasn't yet understood the math involved.

Infinity has been reached sir. Write a 1.
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Zarel
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### Re: Is 0.9 recurring equal to 1?

Sapient wrote:If I write a symbol on a board then we must both be in agreement what precise meaning is represented by that symbol before any tautology can be established. In computer science, limitations of numeric storage are by necessity a consideration during implementation. So I would debate your assertion that there is no recognized area of mathematics where 0.9 recurring is not equal to 1.
Well, yes. In mathematics, the tautology arises from the implicit givens.

"1 + 1 = 2" is meaningless without the implicit context, which is:

"Given [insert rigorous algebraic construction of the real numbers here] and [insert rigorous construction of the addition and equality operators here], 1 + 1 = 2."

It'd also be enough to construct the positive integers, or any other superset, such as the surreal numbers or ZFC.

I'm not sure what you mean by computer science. Computer science is a science, not a branch of math. Sure, there are parts of CS that count as math, such as coding theory, information theory, automata theory, but IEEE 754 Floating Point Math is not a real branch of math (kind of like how Dr. Mario is not a real doctor).

Furthermore, "recurring" is an undefined operation in IEEE 754 Floating Point. It's like contesting "There is no recognized area of mathematics where the square root of 2 is not i" because it's undefined in the real numbers. Obviously we're excluding branches in which it's undefined.

Furthermore,

Code: Select all

``````#include <stdio.h>

int main(void)
{
printf("%d\n", 0.9999999999999999999999999999999999999f == 1.0f);
return 0;
}``````
outputs

Code: Select all

``1``
So, yeah, you're wrong three different ways.
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Midnight_Carnival
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### Re: Is 0.9 recurring equal to 1?

Numbers are abstract concepts, though, but they're rigorous abstract concepts, not vague concepts like "good" and "evil".
...values you can assign arbitrarily to anything you like (hence the one nation rambling and the race troll, and the global warming troll, religion troll... )
mathematics is the only discipline in which absolute truth exists.
...that and delusion.
since maths are an exact(well, however it is said it can never be wrong) science, and there does not matter if you think something is wrong or not, it is either wrong or not independently of human thoughts.
You can't be exact ever, hence the need to invent mathematics and claim "now we have exact values", the argument that mathematics, logic and many other things are universal principles of the universe is BS. They are limitations to our perception, especially if they are treated as solid and untouchable. If it's real, you can touch it, if you can't touch it and it can't touch you it probably doesn't matter.
"correct" and "incorrect" are similarly abstract judgements/concepts,etc... which can be arbitrarily applied to anything. "misuse" is use which the people around you don't agree with.

"1+1=2" is as meaningful as saying " black cats are evil" or "4 is a lucky number".
No offense, but, regardless of the need to pretend we can have absolute clearly defined values interacting in a structured way in order to bypass a lot of pointless speculation, certain claims are best left to the highly religious, and mathematics makes a <urine>-poor religion.

My views on wheter 0.9(rec) = 1 or not:
With my "one nation" rambling, I demostrated how one billion can = 1, therfore, I argue that 0.9(rec) = 1, if it is generally agreed. Mathematics is a system of conventions, conventions change with the times or they are abandoned.
-bye.
...apparenly we can't go with it or something.
pauxlo
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### Re: Is 0.9 recurring equal to 1?

Sapient wrote:If I write a symbol on a board then we must both be in agreement what precise meaning is represented by that symbol before any tautology can be established. In computer science, limitations of numeric storage are by necessity a consideration during implementation. So I would debate your assertion that there is no recognized area of mathematics where 0.9 recurring is not equal to 1.
Now, if you only have limitations of numeric storage, you simply can't store "0.9 recurring" (as a number). The next representable number smaller than 1 may have the representation 0.9999999...999 (if you use some decimal format), but it is not "0.9 recurring".
Darkmage
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### Re: Is 0.9 recurring equal to 1?

Midnight_Carnival wrote:"correct" and "incorrect" are similarly abstract judgements/concepts,etc... which can be arbitrarily applied to anything. "misuse" is use which the people around you don't agree with.

"1+1=2" is as meaningful as saying " black cats are evil" or "4 is a lucky number".
No offense, but, regardless of the need to pretend we can have absolute clearly defined values interacting in a structured way in order to bypass a lot of pointless speculation, certain claims are best left to the highly religious, and mathematics makes a <urine>-poor religion.

Well, 1st of all, correct and incorrect are not that "abstract", it is "abstract", though, if an action is morally correct or incorrect, but if we use a method we can use that method correctly or not.[Those are two different meanings.]

2nd, about 1+1=2 having "no meaning" I got to disagree, maths are a method, we stablish that a unity is equal to 1 and the double of that is 2 and so on with the rest of the numbers, also with the operations, as + is the add, so just adding 1 to 1 is the double, so is 2, empirically, just take a pen, define a pen as 1, then, take a couple of pens and define it as 2, you wil notice that 1 + 1 equals 2, that is true. On the other hand you are telling math can become a religion, I guess you meant that it can become an unfounded belief, mut maths are not that, you can be given some formulas, but those formulas are the shortened path of more complex operations that you can ask and be answered, you only got to take some basis, but again is not nonsense basis(no offend), you just set a symbol for an idea, for the sake of communication, we do not tell you believe in 1=0'9~ because I say so, and then, go everynight an pray to the numbres and all that "religious" stuff, we just tell:

Do this operations: 1/3 = 0'3~ (that's right, right?)

Now try this: 3*0'3~ = 0,9~ (Is this ok?)

Then we will try something different: (1/3)*3 = 3/3 (I guess nothing's wrong here.)

So, we will make final deduction, 3/3 = 1, then 0.9~ = 1 We did the same operation in different ways.

So, the only option left is to say maths do not work properly, they are highly susceptible to be wrong at their claims of exactitude, is a science that fails at his purpose, it is just useless and we should prevent it's propagation. (Irony)

Edit: Also what you say about real/unreal, it does not mean directly for which you can or can't see, you can see many things that are not real but you think they are, for example, a delusion; also numbers are not the real thing you can see, they are concepts. If you state that non-visible things do not exist, tell me how do you see love, satisfaction, and so on..
Tonepoet
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### Re: Is 0.9 recurring equal to 1?

Okay so numbers are representations. Then I have a question about a concept I want to represent: If we don't have issues of numeric storage to consider, how close can we get to 1 without being 1 on the numeric scale? It would seem to me that the best form of representing such an indefinite concept would be to use a similarly indefinite number like .9~ but if .9~ is 1, to answer the question like that should be incorrect. Right?
Last edited by Tonepoet on July 5th, 2010, 2:56 pm, edited 2 times in total.
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Darkmage
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### Re: Is 0.9 recurring equal to 1?

Tonepoet wrote:Okay so numbers are representations. Then I have a question about a concept I want to represent; if we don't have issues of numeric storage to consider, how close can we get to 1 without being 1 on the numeric scale? It would seem to me that the best form of representing such an indefinite concept would be to use a similarly indefinite number like .9~ but since .9~ is 1, to answer the question like that should be incorrect. Right?

Touche!!(Good point)

Counter-question, what is the number following 4? Or either, the one following 1?

I guess that's a problem, we could say lim x --> 1 for x(i do not know better way to explain limits), which would mean that the numbers get infinetly close to 1 but never reaching.
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### Re: Is 0.9 recurring equal to 1?

Then I have a question about a concept I want to represent; if we don't have issues of numeric storage to consider, how close can we get to 1 without being 1 on the numeric scale?
The answer is 1 - ö, where ö is the smallest possible number that is larger than 0. What ö actually is, is a subject for another thread, however.
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### Re: Is 0.9 recurring equal to 1?

Assuming ö exists in the first place.
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Zarel
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### Re: Is 0.9 recurring equal to 1?

Midnight_Carnival wrote:...values you can assign arbitrarily to anything you like (hence the one nation rambling and the race troll, and the global warming troll, religion troll... )
Yes, but the assignment is what's arbitrary, not the values themselves.

You can argue as much as you want that definition of the symbol "1" to denote the mathematical concept "1" is not intrinsic, but that doesn't change the fact that the mathematical concepts stay the same.

You can say

1 + 1 = 2
one plus one equals two

carrot plantain carrot grass tomato

The symbols and words can change, but the meaning behind them stays the same, and the meaning behind them is what's pure, perfect, tautological, exact, absolute mathematical truth. Sure, you can invent a new language (let's call it Middish) in which "one plus one equals two" is false, because in Middish, "plus" means "minus". But that doesn't change the fact that 1+1=2.
Midnight_Carnival wrote:...that and delusion.
Delusion isn't a discipline.
Midnight_Carnival wrote:You can't be exact ever, hence the need to invent mathematics and claim "now we have exact values", the argument that mathematics, logic and many other things are universal principles of the universe is BS. They are limitations to our perception, especially if they are treated as solid and untouchable. If it's real, you can touch it, if you can't touch it and it can't touch you it probably doesn't matter.
You can't be exact in the real world, but that's why mathematics is abstracted from the real world. I wouldn't say "invent" is the term here... mathematics is fundamental to logic.

Saying that something doesn't matter simply because it can't touch you is absurd. You can't touch E=mc^2, either, but I'm pretty sure you can feel getting blown up by a nuke. Math matters because it can be used to understand the real world, and even to manipulate the world to do what we want.
Midnight_Carnival wrote:"correct" and "incorrect" are similarly abstract judgements/concepts,etc... which can be arbitrarily applied to anything. "misuse" is use which the people around you don't agree with.

That statement is completely meaningless.
Midnight_Carnival wrote:"1+1=2" is as meaningful as saying " black cats are evil" or "4 is a lucky number".
No offense, but, regardless of the need to pretend we can have absolute clearly defined values interacting in a structured way in order to bypass a lot of pointless speculation, certain claims are best left to the highly religious, and mathematics makes a <urine>-poor religion.
What is "meaningful" in this context?

"1+1=2" is an expression of a mathematical fact.

"black cats are evil" is an expression of opinion.

"4 is a lucky number" is an unverifiable factual statement that most scientists agree is false.

They all have meaning, and they're all distinct, but comparing how meaningful they are is comparing apples to oranges.

See what happens when you wax philosophical about things you don't understand? You say things that are pure bull@&\$^. You might fool people who are even more ignorant than yourself, but there are few of those people on this forum.
Midnight_Carnival wrote:My views on wheter 0.9(rec) = 1 or not:
With my "one nation" rambling, I demostrated how one billion can = 1,
No, you have demonstrated how one of one thing can contain a billion of something else.

You have not demonstrated that 1000000000 = 1. You have demonstrated that there exists an s such that |1*s| = 1000000000, which is hardly a surprise to anyone.
Midnight_Carnival wrote:therfore, I argue that 0.9(rec) = 1, if it is generally agreed. Mathematics is a system of conventions, conventions change with the times or they are abandoned.
Therefore, your non-sequitur is just as meaningless.
Sgt. Groovy wrote:
Then I have a question about a concept I want to represent; if we don't have issues of numeric storage to consider, how close can we get to 1 without being 1 on the numeric scale?
The answer is 1 - ö, where ö is the smallest possible number that is larger than 0. What ö actually is, is a subject for another thread, however.
The set of all real numbers less than 1 is an open set - it has no maximum, and its supremum is outside of the set.

The answer to "how close can we get to 1 without reaching 1?" is "as close as you want".

By the same reasoning, "ö" as described above does not exist. There is no such thing as the smallest possible positive number (kind of like how there's no such thing as the largest possible positive number).

Here, I will prove that ö does not exist. This is a proof by contradiction:

Assume that ö is the smallest possible number greater than 0.
ö > ö/2 > 0, therefore ö/2 is the smallest possible number greater than 0, and ö is not the smallest possible number greater than 0.
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Joram
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### Re: Is 0.9 recurring equal to 1?

Okay so numbers are representations. Then I have a question about a concept I want to represent: If we don't have issues of numeric storage to consider, how close can we get to 1 without being 1 on the numeric scale? It would seem to me that the best form of representing such an indefinite concept would be to use a similarly indefinite number like .9~ but if .9~ is 1, to answer the question like that should be incorrect. Right?
Zarel answered this quite beautifully in mathematical terms. To put it another way, there is no number that is as close as possible to 1 without being 1 because you can always get closer.

Again we run into infinity. Whatever number you pick, no matter how close to 1, will have an infinite amount of numbers that are closer to 1. Therefore, to say XXX is as close to 1 as you can get without being 1 is false, no matter what XXX is.

EDIT: I didn't realize that three X's in a row would look quite so much like a model of DNA
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### Re: Is 0.9 recurring equal to 1?

Zarel wrote:Assume that ö is the smallest possible number greater than 0.
ö > ö/2 > 0, therefore ö/2 is the smallest possible number greater than 0, and ö is not the smallest possible number greater than 0.